Geometry Definitions

line

A never-ending straight path

regular polygon

A polygon that has all sides congruent and all angles congruent

rate of change

The change in a quantity over time

side

The segments that form a closed figure

perimeter

the sum of the lengths of the sides of a polygon

space

A boundless three-dimensional set of all points

conjunction

A compound statement formed by joining two statements with the word and

conjecture

A conclusion reached that is based on inductive reasoning

angle

A figure formed by two rays with a common endpoint

altitude

A line segment perpendicular to the base of a figure with endpoints on the base and on the vertex opposite the base

transversal

A line that intersects two or more other lines to form eight or more angles

rhombus

A parallelogram with four congruent sides

rectangle

A parallelogram with four right angles

ray

A part of a line that extends indefinitely in one direction from a fixed point

concave

A polygon for which a point on at least one of its diagonals lies outside the polygon

convex

A polygon for which all diagonals are located in the interior of the polygon

n-gon

A polygon with n sides

regular polyhedron

A polyhedron in which the faces are regular congruent polygons

prism

A polyhedron with two parallel, congruent faces called bases. A solid with the following characteristics: 1. Two faces, called the bases, are formed by congruent polygons that lie in parallel planes. 2. The faces that are not bases, called lateral faces, are formed by parallelograms. 3. The intersection of two adjacent lateral faces are called lateral edges and are parallel segments.

parallelogram

A quadrilateral with both pairs of opposite sides parallel and congruent

kite

A quadrilateral with exactly two distinct pairs of adjacent congruent sides

angle bisector

A ray whose endpoint is the vertex of the angle and is located in the interior of the angle. It separates a given angle into two angles with equal measure.

postulate

A rule of geometry that is accepted as being true without proof

diagonal

A segment joining two nonconsecutive vertices of a polygon. In the figure, is a diagonal

perpendicular bisector

A segment that is perpendicular to another segment and passes through that segment's midpoint

midsegment of a trapezoid

A segment with endpoints that are the midpoints of two sides of a triangle

included side

A side common to two given angles of a triangle

polygon

A simple closed figure in a plane formed by three or more line segments

pyramid

A solid figure that has a polygon for a base and triangles for sides. A pyramid is named for the shape of its base. A solid with the following characteristics: 1. All the faces, except one, intersect at a common point called the vertex. 2. The face that does not intersect at the vertex is called the base. The base is formed by a polygon. 3. The faces meeting at the vertex are called lateral faces. They are formed by triangles.

cylinder

A solid figure whose bases are formed by congruent circles in parallel planes and whose lateral surface is curved. The segment whose endpoints are the centers of the circular bases is called the axis of the cylinder. The altitude is a segment perpendicular to the bases with an endpoint in each base.

polyhedron

A solid with four or more flat surfaces that are polygonal regions

point

A specific location in space with no size or shape

theorem

A statement that can be justified by logical reasoning and must be proven before it is accepted as true

cone

A three-dimensional figure with one circular base and one vertex. A curved surface connects the base and the vertex

reflection

A transformation in which a figure is flipped over a line of symmetry

translation

A transformation in which a figure is slid in any direction

rotation

A transformation in which a figure is turned around a fixed point

isosceles trapezoid

A trapezoid with two congruent legs

equilateral polygon

A triangle having all three sides congruent and all three angles congruent

right triangle

A triangle having one right angle

acute triangle

A triangle in which each angle measures less than 90°

isosceles triangle

A triangle with at least two congruent sides

scalene triangle

A triangle with no congruent sides

equiangular polygon

A triangle with three congruent angles

equiangular triangle

A triangle with three congruent angles

plane

A two-dimensional flat surface that extends in all directions

interior

All points between the two sides of an angle

exterior

All points outside the sides of the angle

included angle

An angle formed by two given sides of a triangle

right angle

An angle that measures exactly 90°

obtuse angle

An angle that measures more than 90° but less than 180°

acute angle

An angle with a measure greater than 0° and less than 90°

point-slope form

An equation of the form y - y1 = m(x - x1), where m is the slope and (x1, y1) is a given point on a nonvertical line

slope-intercept form

An equation of the form y = mx + b, where m is the slope and b is the y-intercept

algebraic proof

An expression consisting of one or more numbers and variables along with one or more arithmetic operations

adjacent angles

Angles that have the same vertex, share a common side, and do not overlap

congruent

Having the same measure

parallel lines

Lines in the same plane that never intersect and have the same slope

perpendicular

Lines which meet to form right angles and whose slopes have a product of -1

midpoint

On a line segment, the point that is halfway between the endpoints

vertical angles

Opposite angles formed by the intersection of two lines

line segment

Part of a line containing two endpoints and all the points between them

corresponding parts

Parts of congruent or similar figures that match

between

Point R is between points P and Q if and only if R, P, and Q are collinear and PR + RQ = PQ

congruent polygons

Polygons that have the same shape and size

vertex

The common endpoint of the rays forming the angle

distance

The distance between two points

base angles

The equal angles formed by the base and the congruent sides of an isosceles triangle

base

The faces on the top and bottom of the figure

edge

The intersection of faces of a three-dimensional figure

median

The middle number in a set of data when the data are arranged in numerical order. If the data has an even number, the median is the mean of the two middle numbers

degree

The most common unit of measure for angles

volume

The number of cubic units needed to fill the space occupied by a solid

area

The number of square units needed to cover a surface enclosed by a geometric figure

orthocenter

The point of concurrency of the altitudes of a triangle

incenter

The point of concurrency of the angle bisectors of a triangle

circumcenter

The point of concurrency of the perpendicular bisectors of a triangle

centroid

The point of intersection of the three medians of a triangle

construction

The process of drawing a figure using only a compass and a straightedge

slope

The ratio of the change in the y-coordinates (rise) to the corresponding change in the x-coordinates (run) as you move from one point to another along a line

sphere

The set of all points in space that are a given distance from a given point, called the center. It has the following characteristics: 1. A radius is a segment whose endpoints are the center and a point on the sphere. 2. A chord is a segment whose endpoints are points on the sphere. 3. A diameter is a chord of the sphere that contains the center.

intersection

The set of elements common to two or more sets as in compound inequalities and Venn diagrams

legs

The sides of a right triangle that form the right angle

converse

The statement formed by exchanging the hypothesis and conclusion of a conditional statement

inverse

The statement formed by negating both the hypothesis and conclusion of a conditional statement

surface area

The sum of the areas of all the faces of a three-dimensional figure

concurrent lines

Three or more lines or segments that meet at a common point

collinear

Three or more points that lie on the same line

segment bisector

To separate something into two congruent parts

complementary angles

Two angles are complementary if the sum of their measures is 90°

supplementary angles

Two angles are supplementary if the sum of their measures is 180°

skew lines

Two nonparallel lines that do not intersect. In the figure, and are skew segments

opposite rays

Two rays that are part of the same line and have only their endpoints in common. In the figure, and are opposite rays

point

a location

coplanar

points that lie oin the same plane

linear pair

points upon a line

undefined terms

points, planes, lines in geometry

face

surface of a figure

circumference

the distance around a circle